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Cancers are driven by alterations in diverse genes, creating dependencies that can be therapeutically targeted. However, many genetic dependencies have proven inconsistent across tumors. Here we describe SCHEMATIC, a strategy to identify a core network of highly penetrant, actionable genetic interactions. First, fundamental cellular processes are perturbed by systematic combinatorial knockouts across tumor lineages, identifying 1,805 synthetic lethal interactions (95% unreported). Interactions are then analyzed by hierarchical pooling, revealing that half segregate reliably by tissue type or biomarker status (51%) and a substantial minority are penetrant across lineages (34%). Interactions converge on 49 multigene systems, including MAPK signaling and BAF transcriptional regulatory complexes, which become essential on disruption of polymerases. Some 266 interactions translate to robust biomarkers of drug sensitivity, including frequent genetic alterations in the KDM5C/6A histone demethylases, which sensitize to inhibition of TIPARP (PARP7). SCHEMATIC offers a context-aware, data-driven approach to match genetic alterations to targeted therapies., Competing Interests: Competing interests: J.H.H. and M.A.W. are former or current employees of Ideaya Biosciences and have an equity interest. T.I. is a member of the Ideaya Biosciences scientific advisory board and has an equity interest. T.I. is also a co-founder and member of the advisory board and has an equity interest in Data4Cure and Serinus Biosciences. The terms of these arrangements have been reviewed and approved by the UCSD in accordance with its conflict-of-interest policies. B.M.K. is an employee of Vividion Therapeutics and has equity interests in Pfizer and Vividion Therapeutics. The other authors declare no competing interests., (© 2024. The Author(s), under exclusive licence to Springer Nature America, Inc.)